The present invention relates generally to tomographic imaging and, more particularly, to reprojection and backprojection of tomographic images with hexagonal segmentation. The invention is applicable with tomographic imaging systems such as those used for medical imaging as well as those used for package/baggage security screening systems, non-destructive evaluation, or any other application domain requiring projection or backprojection.
A number of imaging modalities, such as computed tomography (CT), positron emission tomography (PET), single photon counting tomography (SPECT), electrical impedance tomography (EIT), optical tomography, and certain acquisition methods for magnetic resonance imaging (MRI) utilize tomographic reconstruction techniques. Generally, in tomographic reconstruction, tomographic images are created from line or plane integral measurements of an object at a number of orientations. These integral measurements are then processed to yield an image of the object. Projection data is collected into a sinogram that is processed and backprojected to yield the image. Customarily, the projection data undergoes a filtering step prior to backprojection to remove blurring in the image that typically results from a simple backprojection. This reconstruction method is called filtered backprojection (FBP). Other reconstruction techniques of interest include but are not limited to iterative reconstruction algorithms such as maximum likelihood approaches or weighted least square approaches. Furthermore, the proposed technique is also useful for simulations and for certain iterative correction algorithms.
Developments in special hardware that exploits the parallelism of the backprojection process have led to reductions in the reconstruction time of tomographic images. However, notwithstanding these developments, the backprojection process has limited the ability to provide near real-time reconstruction of images. As tomographic scanners are being designed to acquire the raw data at an increasingly faster rate, the computational requirements of conventional FBP becomes increasingly problematic and, as such, presents an obstacle to real-time imaging. More importantly, for iterative reconstruction—which is already routinely used in emission tomography today—the computational requirements are one or two orders of magnitude higher than for FBP.
In this regard, streamlining the projection and backprojection process (PBP) is increasingly garnering the efforts of researchers and engineers. As such, a number of relatively fast reconstruction algorithms have been developed to reduce reconstruction time. In conventional backprojection (or equivalently reprojection), the required number of operations is proportional to N3 for a single 2D image with N×N square pixels and N views. For some fast backprojection techniques, the order of magnitude of the number of operations for a single 2D image with N×N pixels and N views has been reduced to N2log2N. However, while the PBP process has been quickened, image quality and/or image accuracy has degraded. In one proposed PBP technique, a sinogram is recursively subdivided into a series of subsinograms with each subsinogram corresponding to a single pixel (or relatively small number of pixels) of a pixelated image. A pixel is conventionally understood to be a square picture element. While this proposed PBP technique reduces image reconstruction time, e.g., by a factor of N2log2N, the square pixels that the subsinograms represent result in less than ideal coverage of a circular field-of-view (FOV). So the existing fast algorithms are also sub-optimal in this sense. Furthermore, as is appreciated by those skilled in the art, square pixel grids do not provide the optimal sampling in the frequency domain for images, which tend to have a spherical support. This suboptimal sampling can also reduce image quality.
Therefore, it would be desirable to design an apparatus and method of fast PBP that provide further reductions in reconstruction time or that result in improved image quality, and that better covers a circular field of view.